A recent trend in condensed matter physics is that of taking systems out-of-equilibrium. In such a setting, physical phenomena are possible that do not have equilibrium counterparts. Two typical scenarios for non-equilibrium physics are that of open systems, i.e. systems that couple to an environment, and that of quenches, where the system is suddenly taken out-of-equilibrium and its relaxation is studied. The present dissertation addresses three questions, two of which deal with these two scenarios of non-equilibrium situations. The third question is slightly orthogonal, and asks about the potential applications of machine learning to condensed matter physics.
As the first question, we asked about the fate of one dimensional symmetry protected topological (SPT) states when coupled to an environment. By showing how to extend the concept of entanglement spectra for pure states to that of mixed states, we were able to identify genuine mixed states with the properties of topologically non-trivial states. Additionally, we showed how to extend the classification scheme of SPT states based on projective symmetry representations to open systems. As an example, we have also considered the evolution of initial states that are topologically non-trivial upon coupling them to an environment. We have found that the topological non-trivial nature of the state dissapears on the way to reaching a steady state.
As the second question, we asked about the relaxation to equilibrium of a single spin probe coupled to an environment. We showed that the transient behaviour of the de-coherence of this probe spin can be used to investigate an interacting and disordered spin chain. For weak disorder this spin chain is in a thermalizing phase, whereas for strong disorder the system avoids thermalization and instead forms a many-body localized (MBL) phase. We showed that the de-coherence properties of the spin probe provide an unambiguous signal of the MBL phase. This work provides an important experimental probe for investigating the properties of many-body quantum systems further.
For the third question, we considered an equilibrium scenario and asked what potential use a machine learning algorithm can be for such cases. We showed that by compressing the information of the wave function in the form of the entanglement spectrum, it is possible to detect phase transitions using an approach based on artificial neural networks. The application of machine learning techniques to condensed matter physics is a very novel trend, and it is a fast-moving subject. Next to developing our own approach in this dissertation, we provide an overview of the recent works, thereby giving an understanding of the potential uses of machine learning in condensed matter physics.
These three projects together, each in their own right, address important questions in condensed matter physics. Each of them deals with a recent topic that is of interest to a broad community, and provides non-trivial results that further these communitiesShow more